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The paradoxical zero reflection at zero energy

Authors
  • Ahmed, Zafar
  • Sharma, Vibhu
  • Sharma, Mayank
  • Singhal, Ankush
Type
Preprint
Publication Date
May 24, 2016
Submission Date
May 24, 2016
Identifiers
arXiv ID: 1605.07315
Source
arXiv
License
Yellow
External links

Abstract

Earlier, using the peculiar attractive double Dirac delta potential, zero reflection at zero energy ($R(0)=0$) has been revealed. However, in doing so the most common potentials have been ignored and for an arbitrary potential well the proof is lengthy and less transparent. Here, we give a simple proof that when one-dimensional attractive scattering potential well $V(x)$ possesses a half-bound state at energy $E=0$, $R(0)$ is 0 when $V(x)$ is symmetric and it is less than 1 when $V(x)$ is asymmetric. We also demonstrate these paradoxical results in the most common potential wells.

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